Power light blinking yellow after sitting a while
Unplug computer, disconnect all usb/monitor/internet, open it, hold power button until green led on the inside on the motherboard turns off, pop out the BIOS battery (looks like a big watch battery and use a small flathead screwdriver to depress the spring lock on one side), plug in computer, hold power button for about 20 seconds (must reset BIOS or something), let up on power button, wait 10 seconds and push power button. The computer should turn on. Wait for it until activity seems stable (1 min. or so). Push powerbutton to shut off.
If this has worked you have proven that it's not the power supply (it turned on).
Go buy a new battery (CR2032 3 volt). Unplug computer, open it, hold power button until green led on the inside on the motherboard turns off, pop in new battery, plug in (you should notice the power button blinking amber again), hold power button until it stops blinking (about 20 sec....again must reset BIOS or something), wait 10 sec., push power button. the computer should turn on. Wait for it until activity seems stabe (1 min. or so). Push powerbutton to shut off.
Now, close case, plug in all usb/monitor/internet/etc. Power up computer. You'll get an internal floppy drive error. Push F2 (maybe F1) to get into the BIOS settings and go to "drives" and turn off the internal floppy. Save and exit. The computer should boot properly now.
This seems to be a big problem with the e510, my theory is that this one small battery is the root of most of these failures (as these computers usually fail after 1-2 years), not the power supply or the motherboard (heck, when you replace the motherboard it comes with a new one of these batteries...a several hundred dollar piece of hardware, with a $5 battery that will actually fix it).